A smog alert is issued when the amount of particualte matterin the air is found

Question

A smog alert is issued when the amount of particualte matterin the air is found to be greater than 7ppm. Samples collected from16 stations have a mean of 7.8ppm and a standard deviation of2ppm. a.) report a 95% one sided confidence interval for the meanparticulate in the air b.) Perform a post- hoc power analysis. Compute the differencefor which you have 80% power with a sample size of n= 16stations. A smog alert is issued when the amount of particualte matterin the air is found to be greater than 7ppm. Samples collected from16 stations have a mean of 7.8ppm and a standard deviation of2ppm. a.) report a 95% one sided confidence interval for the meanparticulate in the air b.) Perform a post- hoc power analysis. Compute the differencefor which you have 80% power with a sample size of n= 16stations.

Explanation / Answer

Null hypothesis, H0: 7
Alternate hypothesis, H1: > 7

sample mean, x = 7.8
sample standard deviation, s = 2
sample size, n = 16
standard error, e = s/n = 2/16 =0.5

test statistics , t = (x-)/e = (7.8-7)/0.5=1.6

degrees of freedom, df = n-1=16-1=15
At = .05, df = 15 and one tail,
critical t from the t table = 1.753

since the test statistics is less than the critical t value, hencewe accept the null hypothesis.

hence, we can conclude that A smog alert need not be issued as theamount of particualte matter in the air is found to be less than7ppm

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